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A289971 Number of permutations of [n] determined by their antidiagonal sums. 3
1, 1, 2, 4, 9, 20, 49, 114, 277, 665, 1608, 3875 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
C. Bebeacua, T. Mansour, A. Postnikov, and S. Severini, On the X-rays of permutations, arXiv:math/0506334 [math.CO], 2005.
FindStat - Combinatorial Statistic Finder, The number of permutations with the same antidiagonal sums.
Martin Rubey, Alternating Sign Matrices Through X-Rays, J. Int. Seq., Vol. 24 (2021), Article 21.6.5.
MATHEMATICA
xray[perm_List] := Module[{P, n = Length[perm]}, P[_, _] = 0; Thread[perm -> Range[n]] /. Rule[i_, j_] :> Set[P[i, j], 1]; Table[Sum[P[i - j + 1, j], {j, Max[1, i - n + 1], Min[i, n]}], {i, 1, 2n - 1}]];
a[n_] := xray /@ Permutations[Range[n]] // Tally // Count[#, {_List, 1}]&;
Do[Print[n, " ", a[n]], {n, 0, 10}] (* Jean-François Alcover, Feb 28 2020 *)
PROG
(Sage)
def X_ray(pi):
P = Permutation(pi).to_matrix()
n = P.nrows()
return tuple(sum(P[k-1-j][j] for j in range(max(0, k-n), min(k, n)))
for k in range(1, 2*n))
@cached_function
def X_rays(n):
return sorted(X_ray(pi) for pi in Permutations(n))
def statistic(pi): return X_rays(pi.size()).count(X_ray(pi))
[[statistic(pi) for pi in Permutations(n)].count(1) for n in range(7)]
CROSSREFS
Sequence in context: A000081 A124497 A286983 * A093637 A068051 A032289
KEYWORD
nonn,more
AUTHOR
Martin Rubey, Jul 16 2017
EXTENSIONS
a(8)-a(11) from Alois P. Heinz, Jul 24 2017
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)